The length and breadth of a rectangle are in the ratio 9 : 5. If its area is 720 `m^(2)`, find its perimeter.

Options

A. 112 metre
B. 115 metre
C. 110 metre
D. 118 metre

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Ratio
The length and breadth of the rectangle are in the ratio 9:5. We can express the length and breadth in terms of a variable \( x \):
- Length \( L = 9x \)
- Breadth \( B = 5x \)

**Hint:** Remember that ratios can be represented using a common variable.

### Step 2: Use the Area Formula
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the expressions for length and breadth, we have:
\[ A = (9x) \times (5x) = 45x^2 \]

**Hint:** The area formula is essential for finding the dimensions of the rectangle.

### Step 3: Set Up the Equation
We know the area of the rectangle is given as 720 m². Therefore, we can set up the equation:
\[ 45x^2 = 720 \]

**Hint:** Equate the expression for area to the given area to find \( x \).

### Step 4: Solve for \( x^2 \)
To find \( x^2 \), divide both sides of the equation by 45:
\[ x^2 = \frac{720}{45} \]
Calculating the right side:
\[ x^2 = 16 \]

**Hint:** Simplifying fractions can help in finding the value of \( x \).

### Step 5: Find \( x \)
Now, take the square root of both sides to find \( x \):
\[ x = \sqrt{16} = 4 \]

**Hint:** Remember that the square root gives you the positive value since dimensions cannot be negative.

### Step 6: Calculate Length and Breadth
Now that we have \( x \), we can find the length and breadth:
- Length \( L = 9x = 9 \times 4 = 36 \) m
- Breadth \( B = 5x = 5 \times 4 = 20 \) m

**Hint:** Substitute \( x \) back into the expressions for length and breadth to find their actual values.

### Step 7: Calculate the Perimeter
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]
Substituting the values we found:
\[ P = 2 \times (36 + 20) = 2 \times 56 = 112 \text{ m} \]

**Hint:** The perimeter formula involves adding the length and breadth before multiplying by 2.

### Final Answer
The perimeter of the rectangle is **112 meters**.

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